Research On The Relevant Problems Of Markov Dependentstructural Risk Model

The Cramer-Lundberg model is a classical risk model established by Swedish actuary Lundberg and Cramer based on rigorous mathematics.The classical risk model is the simplest and most widely used risk model.In recent years,with the improvement of living standards,the insurance market has gradually expanded,and people's demands for insurance are increasing.In the daily operation of an insurance company,it is necessary to assess the stability of its business.On the other hand,for investors,the economic strength of an insurance company is particularly important,and the economic strength of an insurance company can be distributed through the insurance company and the issuance of stocks,incorrect dividend distribution and stock issuance will also lead to the bankruptcy of insurance companies,which caused dividend policy came into being.In the classic risk model,people only study the most basic and essential factors of insurance companies,and they lack effective research on the risks faced by insurance companies.In this paper we generalize the existing risk models under the actual situation faced by insurance companies is considered.Considering the ruin probability problem under a special kind of conversion density,by defining the conversion density of the dependent structure,the Markov chain correlation theory is applied to its correlation calculation,and the display expression of the ruin probability in the case of incremental dependence is obtained,and the result is extended to the.more complex risk measure discount penalty function in risk theory.On the other hand,we consider the demand of dividends for inv estors and the requirements of insurance companies for their own stability,the insurance company's dividend policy under the Markov modulation risk model is studied,and give the corresponding strategies.The basic framework of the article is as follows:In chapter one,we summarize the development process of the risk model,and the research status at home and abroad related to the content are briefly reviewed,finally summarizes the main research contents of this paper.In chapter two,we introduce some useful basic theoretical knowledge,including the basic theory and knowledge of risk model,optimal dividend problem,Markov chain and so on.In chapter three,based on the classical risk model,we study the ruin probability problem of the Markov structure risk model under stochastic premium income.We assume that the net loss has Markov property and defines the conversion density of the dependent structure.By applying the Markov chain theory to its correlation calculation,the explicit expression of ruin probability in the case of incremental dependence is obtained and extended to the discount penalty function.In chapter four,considering the stochastic disturbance factors,we study the optimal dividend policy under Markov chain dependent structure model,the HJB equation of value function is given by using the principle of dynamic programming.By verifying the theorem,we obtain the optimal solution of this HJB equation and the optimal dividend policy is obtained.In chapter five,we summarize the research results of this paper,and puts forward the shortcomings of the article and the prospects for the follow-up work.